Cartesian monoidal category

Cartesian categories are cartesian monoidal categories. Their multicategorical analogues are cartesian multicategories.

Fox’s theorem characterizes cartesian monoidal categories as those with tensor-compatible comonoids (and can be refined to comagmas).

See also.

• Fox’s theorem and cocommutativity
• Refining Fox’s Theorem
• uniform copy delete
• Cartesian by split
• Cartesian, partial and deterministic